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5(x-4)(4x+5)=0

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Solution for 5(x-4)(4x+5)=0 equation:



5(x-4)(4x+5)=0
We multiply parentheses ..
5(+4x^2+5x-16x-20)=0
We multiply parentheses
20x^2+25x-80x-100=0
We add all the numbers together, and all the variables
20x^2-55x-100=0
a = 20; b = -55; c = -100;
Δ = b2-4ac
Δ = -552-4·20·(-100)
Δ = 11025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}

\sqrt{\Delta}=\sqrt{11025}=105
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-105}{2*20}=\frac{-50}{40} =-1+1/4
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+105}{2*20}=\frac{160}{40} =4

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